采用地统计学的变异函数分析方法定量研究了落叶松（Larix olgensis）纯林表层（0～10 cm）细根的空间异质性特征，利用地统计学的克里格内插法结合定积分，对落叶松纯林表层细根（<2 mm）的生物量进行了估测。结果表明：1）6种林龄（14～40 年）的落叶松人工纯林表层细根的变异函数曲线理论模型均为球状模型，空间变异主要是由结构性因素引起，且空间自相关程度均属中等以上（空间结构比>25%）。14、19、22、26、32、40年生的落叶松纯林表层细根的空间变异尺度分别为1.76、3.40、1.02、4.12、3.37和5.58 m。在所研究的林龄范围内，随林龄的增长，落叶松纯林表层细根的空间变异尺度近似呈直线增长（p =0.074 4）。2）非参数统计的成对样本符号检验结果表明，变异函数分析结果基础上的克里格内插法适用于落叶松纯林表层细根生物量的估计。利用此估计值，拟合其与位置坐标值之间的多元回归关系均为二元十次余弦级数多项式。利用此多项式，通过定积分的方法（积分区间为整块样地的大小），估计出14、19、22、26、32、40年生的落叶松纯林表层细根生物量分别为1.097 3、1.434 0、1.185 4、0.974 3、1.682 6、1.255 6 Mg• hm-2。3）在本次调查的林龄范围内（14～40年），落叶松纯林表层细根的现存量近似相等（α=0.037 3），土壤表层单株细根生物量与林龄之间呈极显著的指数增长关系（α =0.002）。4）采用地统计学的克里格空间插值，结合多元回归和定积分的方法，可以实现落叶松人工林表层细根生物量的准确估计。
Background and Aims Drilling soil core, simply averaging the surveying values and ignoring the information of sampling point locations are in common use in estimating the fine root biomass of forest. Owing to the significant heterogeneity of fine root distribution, using the method above may be not proper. The Larix olgensis stand was chosen for a case study. Answer to the following question was sought: is the fine root biomass estimated by combining the coordinates of sampling points.
Methods Semivariance analysis of Geostatistics was used to quantify the spatial heterogeneity of fine root (<2 mm) biomass in upper layer of soil (0-10 cm) in Larix olgensis stand (14-40 year). Fine root biomass was estimated with kriging interpolation of Geostatistics and definite integral.
Key Results The semivariograms of fine roots in all six Larix olgensis stands were best described by spherical model. The spatial variability of fine root in all six Larix olgensis stands was mainly caused by structural factors with spatial structural ratio >25 %. The scales of spatial heterogeneity of fine roots (1. 76-5.58 m) showed a positive linear correlation (p＝0.074 4) with stand age (14-40 year). The sign_test of nonparametric statistics of paired samples showed that the kriging interpolation, based on the results of semivariance analysis, could be used to estimate the fine root biomass in Larix olgensis stands. The relationship between the estimated fine root biomass and the values of its corresponding coordinates was best fitted by bivariate order 10 cosine series polynomial. Based on the result of definite integral to those polynomials (integral range was limited to plot size), total fine root biomass of the 14_year, 19_year, 22_year, 26_year, 32_year, 40_year_old stands was 1.097 3, 1.434 0, 1.185 4, 0.974 3 , 1. 682 6, 1.255 6 Mg•hm-2, respectively. No differences (α=0.037 3 ) were found in the fine root biomass in upper soil layer of Larix olgensis stands with difference stand ages. The estimated of fine root mass of individual stems increased exponentially with stand age (α=0.002).
Conclusions Kriging interpolation method of Geostatistics, combined with multiple regression and definite integral, provide a new optimal alternative for the estimation of fine root biomass in Larix olgensis stands.